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vishal.pathak
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|x+2|=|y+2| what is the value of x+y?
(1) xy<0
If the product is negative, then one of our variables is positive and the other is negative. If x=4, then y=-8. 4 + -8= -4. If x=-8, then y=4. -8 + 4 = -4. Sufficient since we get the same value each time.
(2) x>2 y<2
Our first example from statement 1 meets these requirements, so we can reuse it. If x=4, then y=-8. 4 + -8 = -4. If x =8, then y = -12. 8 + -12 = -4. Sufficient since we get the same value each time.
The correct answer is D.
Is |x+y|>|x-y|?
(1) |x| > |y|
If x=6 and y=4, then abs(6+4)=10 and abs(6-4)=2. YES
If x=2 and y=0, then abs(2+0)=2 and abs(2-0)=2. NO
Insufficient
(2) |x-y| < |x|
Our first example from statement 1 still holds: abs(6-4)=2, abs(6)=6
If x=6 and y=4, then abs(6+4)=10 and abs(6-4)=2. YES
If x=-4 y =-2, abs(-4 - -2) = 2, abs(-4)=4
abs(-4 + -2)=6, abs(-4 - -2) = 2. YES
Essentially, Statement 2 rules out the possibility that y=0 (which is what made the first statement insufficient), which allows us to answer with a definitive yes. Sufficient, so the correct answer is B.
Bill
